This article is about NOR Logic in the sense of building other logic gates using just NOR gates. For NOR gates, see
NOR gate. For NOR in the purely logical sense, see
Logical NOR. For logic gates in general, see
Logic Gate.
A single NOR gate
A NOR gate is a logic gate which gives a positive output only when both inputs are negative.
Like NAND gates, NOR gates are so-called "universal gates" that can be combined to form any other kind of logic gate. For example, the first embedded system, Apollo Guidance Computer, was built exclusively from NOR gates, about 5,600 in total for the later versions. Today, integrated circuits are not constructed exclusively from a single type of gate. Instead, EDA tools are used to convert the description of a logical circuit to a netlist of complex gates (standard cells) or transistors (full custom approach).
NOR
A NOR gate is logically an inverted OR gate. By itself has the following truth table:
|
Truth Table
| Input A | Input B | | Output Q |
|---|
| 0 | 0 | | 1 |
| 0 | 1 | | 0 |
| 1 | 0 | | 0 |
| 1 | 1 | | 0 |
|
Making other gates by using NOR gates
A NOR gate is a universal gate, meaning that any other gate can be represented as a combination of NOR gates.
This is made by joining the inputs of a NOR gate. As a NOR gate is equivalent to an OR gate leading to NOT gate, this automatically sees to the "OR" part of the NOR gate, eliminating it from consideration and leaving only the NOT part.
output= NOT(A+A)
| Desired Gate | NOR Construction |
|---|
 |  |
Truth Table
| Input A | | Output Q |
|---|
| 0 | | 1 |
| 1 | | 0 |
|
The OR gate is simply one NOR gate followed by a second whose inputs are joined.
Output= NOT[NOT(A+B)+NOT(A+B)]
| Desired Gate | NOR Construction |
|---|
 |  |
Truth Table
| Input A | Input B | | Output Q |
|---|
| 0 | 0 | | 0 |
| 0 | 1 | | 1 |
| 1 | 0 | | 1 |
| 1 | 1 | | 1 |
|
An AND gate gives a 1 output when both inputs are 1; a NOR gate gives a 1 output only when both inputs are 0. Therefore, an AND gate is made by inverting the inputs to a NOR gate.
| Desired Gate | NOR Construction |
|---|
 |  |
Truth Table
| Input A | Input B | | Output Q |
|---|
| 0 | 0 | | 0 |
| 0 | 1 | | 0 |
| 1 | 0 | | 0 |
| 1 | 1 | | 1 |
|
A NAND gate is made using an AND gate in series with a NOR gate:
| Desired Gate | NOR Construction |
|---|
 |  |
Truth Table
| Input A | Input B | | Output Q |
|---|
| 0 | 0 | | 1 |
| 0 | 1 | | 1 |
| 1 | 0 | | 1 |
| 1 | 1 | | 0 |
|
An XOR gate is made by connecting the output of 3 NOR gates (connected as an AND gate) and the output of a NOR gate to the respective inputs of a NOR gate. This expresses the logical formula (A AND B) NOR (A NOR B). This construction entails a propagation delay three times that of a single NOR gate.
| Desired Gate | NOR Construction |
|---|
 |  |
Truth Table
| Input A | Input B | | Output Q |
|---|
| 0 | 0 | | 0 |
| 0 | 1 | | 1 |
| 1 | 0 | | 1 |
| 1 | 1 | | 0 |
|
An XNOR gate can be constructed from four NOR gates implementing the expression "(A NOR N) NOR (B NOR N) where N = A NOR B".This construction has a propagation delay three times that of a single NOR gate, and uses more gates.
| Desired XNOR Gate | NOR Construction |
|---|
 |  |
Truth Table
| Input A | Input B | | Output Q |
|---|
| 0 | 0 | | 1 |
| 0 | 1 | | 0 |
| 1 | 0 | | 0 |
| 1 | 1 | | 1 |
|
See also
References